WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERóN-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES

Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.

Boundedness of Multilinear Singular Integrals and Their Commutators on Morrey-Herz Spaces with Non-doubling Measures

Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.

BOUNDEDNESS OF VECTOR-VALUED CALDERN-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES

In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q（R^d,｜x｜^α d μ）space, with 1〈q〈∞,-n〈α〈n（q-1）,and on L^1,∞ （R^d,｜x｜^α d μ）space,with -n〈α〈0.

Iterated Commutators for Multilinear Singular Integral Operators on Morrey Space with Non-Doubling Measures

Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

A Synergistic Multi-Attribute Decision-Making Method for Educational Institutions Evaluation Using Similarity Measures of Possibility Pythagorean Fuzzy Hypersoft Sets

Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be difficult.The concept of a possibility Pythagorean fuzzy hypersoft set(pPyFHSS)is more flexible in this regard than other theoretical fuzzy set-like models,even though some attempts have been made in the literature to address such uncertainties.This study investigates the elementary notions of pPyFHSS including its set-theoretic operations union,intersection,complement,OR-and AND-operations.Some results related to these operations are also modified for pPyFHSS.Additionally,the similarity measures between pPyFHSSs are formulated with the assistance of numerical examples and results.Lastly,an intelligent decision-assisted mechanism is developed with the proposal of a robust algorithm based on similarity measures for solving multi-attribute decision-making(MADM)problems.A case study that helps the decision-makers assess the best educational institution is discussed to validate the suggested system.The algorithmic results are compared with the most pertinent model to evaluate the adaptability of pPyFHSS,as it generalizes the classical possibility fuzzy set-like theoretical models.Similarly,while considering significant evaluating factors,the flexibility of pPyFHSS is observed through structural comparison.

Voices that matter:The impact of patient-reported outcome measures on clinical decision-making

The critical role of patient-reported outcome measures(PROMs)in enhancing clinical decision-making and promoting patient-centered care has gained a profound significance in scientific research.PROMs encapsulate a patient's health status directly from their perspective,encompassing various domains such as symptom severity,functional status,and overall quality of life.By integrating PROMs into routine clinical practice and research,healthcare providers can achieve a more nuanced understanding of patient experiences and tailor treatments accordingly.The deployment of PROMs supports dynamic patient-provider interactions,fostering better patient engagement and adherence to tre-atment plans.Moreover,PROMs are pivotal in clinical settings for monitoring disease progression and treatment efficacy,particularly in chronic and mental health conditions.However,challenges in implementing PROMs include data collection and management,integration into existing health systems,and acceptance by patients and providers.Overcoming these barriers necessitates technological advancements,policy development,and continuous education to enhance the acceptability and effectiveness of PROMs.The paper concludes with recommendations for future research and policy-making aimed at optimizing the use and impact of PROMs across healthcare settings.

Variations in quantifying patient reported outcome measures to estimate treatment effect

In the practice of healthcare,patient-reported outcomes(PROs)and PRO measures(PROMs)are used as an attempt to observe the changes in complex clinical situations.They guide us in making decisions based on the evidence regarding patient care by recording the change in outcomes for a particular treatment to a given condition and finally to understand whether a patient will benefit from a particular treatment and to quantify the treatment effect.For any PROM to be usable in health care,we need it to be reliable,encapsulating the points of interest with the potential to detect any real change.Using structured outcome measures routinely in clinical practice helps the physician to understand the functional limitation of a patient that would otherwise not be clear in an office interview,and this allows the physician and patient to have a meaningful conver-sation as well as a customized plan for each patient.Having mentioned the rationale and the benefits of PROMs,understanding the quantification process is crucial before embarking on management decisions.A better interpretation of change needs to identify the treatment effect based on clinical relevance for a given condition.There are a multiple set of measurement indices to serve this effect and most of them are used interchangeably without clear demarcation on their differences.This article details the various quantification metrics used to evaluate the treatment effect using PROMs,their limitations and the scope of usage and implementation in clinical practice.

Morrey Spaces for Non-doubling Measures

The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.

Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular integrals are bounded from L 1(μ) × L 1(μ) to L 1/2,∞(μ).

Boundedness of Some Maximal Commutators in Hardy-type Spaces with Non-doubling Measures

Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO（μ） functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO（μ） functions, of the Hardv soace H^I（μ） of Tolsa.

Weighted estimates for commutators of singular integral operators with non-doubling measures

Letμbe a nonnegative Radon measure on R^d which only satisfiesμ(B(x,r))≤C_0r^n for all x∈R^d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions.

Θ-type Calderón-Zygmund Operators with Non-doubling Measures

Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.

Atomic Hardy-type Spaces between H1 and L1 on Metric Spaces with Non-doubling Measures

Let （y, d, dλ） be （Rn, ｜·｜,μ）, where ｜·｜ is the Euclidean distance, μ is a nonnegative Radon measure on Rn satisfying the polynomial growth condition, or the Gauss measure metric space （Rn, ｜·｜,dγ）, or the space （S, d, p）, where S - Rn×R＋ is the （ax ＋ b）-group, d is the left-invariant Riemannian metric and p is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces {Xs（Y））0〈s≤∞ and the BM0-type spaces {BM0（y, s）}0〈s≤∞. Let Hi（Y） be the known atomic Hardy space and L01（y） the subspace of f ∈ L1（Y） with integral 0. The authors prove that the dual space of Xs（Y） is SM0（Y,s） when s∈ （0, ∞）, Xs（Y） = H1（Y） when s ∈ （0, 1], and X∞（y） = L01（Y） （or L1（Y））. As applications, the authors show that if T is a linear operator bounded from H1 （Y） to L1 （Y） and from L1（y） to L1,∞（Y）, then for all r ∈ （1, ∞） and s ∈ （r, ∞], T is bounded from Xr（y） to the Lorentz space L1,8（y）, which applies to the Calderon-Zygmund operator on （Rn, ｜·｜,μ）, the imaginary powers of the 0rnstein-Uhlenbeck operator on （Rn, ｜·｜,dγ） and the spectral operator associated with the spectral multiplier on （S, d, p）. All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces.

Endpoint Estimates for Multilinear Fractional Integrals with Non-doubling Measures

Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with it, which, in the case when μ is the d-dimensional Lebesgue measure, also improve the known results.

Boundedness of Calderon-Zygmund operators with finite non-doubling measures

Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.

HealthMeasures患者报告结局报告清单的解读

美国匹兹堡大学和HealthMeasures指导委员会及PROMIS健康组织标准委员会共同发表了HealthMeasures患者报告结局报告清单,旨在促进不同患者报告结局测量工具的标准化报告,帮助研究人员提高工具报告质量及结果解释的准确性,进一步改善跨研究间的比较分析。本文对HealthMeasures患者报告结局报告清单的主要内容进行介绍和解读,以期为中国患者报告结局研究者提供参考和借鉴。

BOUNDEDNESS OF FRACTIONAL INTEGRALS IN HARDY SPACES WITH NON-DOUBLING MEASURE—In Memory of Professor Sun Yongsheng

Let μ be a Borel measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（Q） ≤ col（Q）^n for any cube Q belong to R^d with sides parallel to the coordinate axes and for some fixed n with 0 〈 n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H^1（μ）.

Practice of Barrier Measures against COVID-19 Among Diabetic People Followed at Departmental University Hospital Center Ouémé-Plateau, Benin, in 2021

Introduction: COVID-19 is a pandemic disease caused by the coronavirus SARS-COV2 appeared in China in 2019. The aim of the study was to evaluate the practice of barrier measures against COVID-19 and to identify associated factors among diabetics followed at Departmental University Hospital Center Ouémé-Plateau, Benin, in 2021. Methods: This was a cross-sectional study conducted from June to August 2021, including diabetics aged 18 and over, hospitalized or received for medical visits in the department of medicine at the target hospital. Data were collected during an interview with each participant thanks to a questionnaire. “Good practice” was defined as regular practice of at least two of three barrier measures: hand washing, physical distancing and mask-wearing. Results: A total of 110 diabetics were included with a female predominance (55.5%) and a mean age of 57 ± 11.3 years. Among them, 89.1% washed their hands, 41.8% respected physical distancing and 12.7% wore a mask. The proportion of good practice was 47.3%. Only 5 practiced the three barrier measures. Only age group was associated with good practice. Conclusion: The study showed a low proportion of good practice of barrier measures against COVID-19 among diabetic people surveyed. It is important to continue the action for COVID-19 prevention among diabetic people in the targeted hospital and in other hospitals in Benin.

Socio-scientific quantification of the comprehensive benefits of debris flow mitigation measures for villages in western Sichuan, China

Debris flow hazards seriously threaten thesafety and sustainable development of mountainousareas. Numerous debris flow mitigation measures havebeen implemented worldwide;however, acomprehensive assessment of the specific disasterreduction effects of these measures and their economic,social and ecological benefits is yet to be performed.The western region of Sichuan Province frequentlysuffers from geohazards such as debris flow, and thegovernment has adopted many mitigation measures.This study assessed the benefits of debris flowmitigation measures and identified the key influencingfactors via a field-based study conducted in 81 villagesin western Sichuan province, China. A framework forthe evaluation of the benefits of rural debris flowmitigation measures was constructed andquantitatively evaluated using a survey. Snowballsampling was performed to recruit 81 village leadersand 468 farmers. The results showed that managementand engineering measures were the main methodsused to mitigate debris flow;ecological measures wereauxiliary. The average satisfaction scores of farmers forthese three types of measures were 4.07, 3.90, and 3.56,respectively (as measured on a five-point Likert scale).In contrast, in terms of the benefits of these mitigationmeasures, only a small proportion of villages (11.11%)obtained a high level of comprehensive benefits fromthe debris flow mitigation measures, while the majority(88.89%) received medium to low-level benefits. Toimprove this situation, we further studied and foundthat the main factors that restricted villages fromachieving high-level comprehensive benefits were theunpredictable nature of debris flows, labour forceoutflow and remoteness. Effective control measures, agood economic environment and strong governmentassistance were reported as crucial factors forimproving these comprehensive benefits. This studyprovides socio-scientific references for decisionmakingon rural debris flow mitigation measures while keeping villages at the centre of economic development.

Adherence to Physical Measures during the SARS-COV2 Pandemic by Haemodialysis Patients in a Burkina Faso Tertiary Hospital: A Cross-Sectional Survey

Context: COVID-19 can spread rapidly in haemodialysis centres, leading to fatal outcomes. Implementing physical measures is crucial in limiting the spread of infection. Aims: To assess adherence to physical measures against SARS-Cov2 in haemodialysis patients. Methods and Material: From 13 to 19 July 2021, we administered the questionnaire to haemodialysis patients during or immediately after the dialysis session. The dependent variables were adherence to wearing masks, hand washing outside the dialysis centre, social distancing of at least 1.5 meters, and cough and sneeze hygiene. Statistical Analysis Used: Data were analyzed using Epi info software;descriptive statistics were presented as mean, headcount, and percentage;related factors were determined by multi-logistic regression. The significance level was 5%. The Health Research Ethics Committee approved the research protocol. Results: 142 patients were included (mean age: 42.5 ± 14 years). Wearing masks, hand-washing, social distancing, and coughing and sneezing hygiene were observed by 88%, 75%, 47%, and 60% of patients, respectively. Conclusion: Wearing masks was the most respected physical measure, while social distancing was the least respected.